pr\u00e9sentent l\u2019AVIS DE SOUTENANCE de Monsieur Cl\u00e9ment FERNANDES<\/p>\n\n\n\n
Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Institut Polytechnique de Paris, pr\u00e9par\u00e9 \u00e0 T\u00e9l\u00e9com SudParis en :<\/p>\n\n\n\n
le LUNDI 21 NOVEMBRE 2022 \u00e0 9h30 \u00e0 E0023
T\u00e9l\u00e9com SudParis, 9 rue Charles Fourier ,91011 Evry Cedex France<\/p>\n\n\n\n
Membres du jury :<\/strong><\/p>\n\n\n\n M. Wojciech PIECZYNSKI<\/strong>, Professeur, T\u00e9l\u00e9com SudParis, FRANCE – Directeur de th\u00e8se R\u00e9sum\u00e9 :<\/strong><\/p>\n\n\n\n Les cha\u00eenes de Markov cach\u00e9es (HMC) sont tr\u00e8s utilis\u00e9es pour la segmentation bay\u00e9sienne non supervis\u00e9e de donn\u00e9es discr\u00e8tes. Elles sont particuli\u00e8rement robustes et, malgr\u00e9 leur simplicit\u00e9, elles sont suffisamment efficaces dans de nombreuses situations. En particulier pour la segmentation d\u2019image, malgr\u00e9 leur nature unidimensionnelle, elles sont capables, gr\u00e2ce \u00e0 une transformation des images bidimensionnelles en s\u00e9quences monodimensionnelles avec le balayage de Peano (PS), de produire des r\u00e9sultats satisfaisants. Cependant, dans certains cas, on peut pr\u00e9f\u00e9rer des mod\u00e8les plus complexes tels que les champs de Markov cach\u00e9es (HMF) malgr\u00e9 leur plus grande complexit\u00e9 en temps, pour leurs meilleurs r\u00e9sultats. De plus, les mod\u00e8les de Markov cach\u00e9s (les cha\u00eenes aussi bien que les champs) ont \u00e9t\u00e9 \u00e9tendus aux mod\u00e8les de Markov couples et triplets, qui peuvent \u00eatre int\u00e9ressant dans des cas plus complexes. Par exemple, lorsque le temps de s\u00e9jour n\u2019est pas g\u00e9om\u00e9trique, les cha\u00eenes de semi-Markov cach\u00e9es (HSMC) ont tendance \u00e0 \u00eatre plus performantes que les HMC, and on peut dire de m\u00eame pour les cha\u00eenes de Markov \u00e9videntielles cach\u00e9es (HEMC) dans le cas de donn\u00e9es non-stationnaires. Dans cette th\u00e8se, nous proposons dans un premier lieu une nouvelle cha\u00eene de Markov triplet (TMC), qui \u00e9tend simultan\u00e9ment les HSMC et les HEMC. Bas\u00e9e sur les cha\u00eenes de Markov triplets cach\u00e9es (HTMC), la nouvelle cha\u00eene de semi-Markov \u00e9videntielle cach\u00e9e (HESMC) peut \u00eatre utilis\u00e9e de mani\u00e8re non supervis\u00e9e, les param\u00e8tres \u00e9tant estim\u00e9s avec l\u2019algorithme Expectation-Maximization (EM). Nous validons l\u2019int\u00e9r\u00eat d\u2019un tel mod\u00e8le gr\u00e2ce \u00e0 des exp\u00e9riences sur des donn\u00e9es synth\u00e9tiques. Nous nous int\u00e9ressons ensuite au probl\u00e8me de l\u2019unidimensionnalit\u00e9 des HMC avec PS dans le cadre de la segmentation d\u2019image, en construisant le balayage de Peano contextuel (CPS). Il consiste \u00e0 associer \u00e0 chaque indexe dans le HMC obtenu \u00e0 partir du PS, deux observations sur les pixels qui sont voisins du pixel en question dans l\u2019image consid\u00e9r\u00e9e, mais qui ne sont pas voisins dans la HMC. On obtient donc trois observations pour chaque point du balayage de Peano, ce qui induit une nouvelle cha\u00eene de Markov conditionnelle (CMC) avec une structure plus complexe, mais dont la loi a posteriori est toujours markovienne. Ainsi, nous pouvons appliquer la m\u00e9thode classique d\u2019estimation des param\u00e8tres : l\u2019algorithme Stochastic Expectation-Maximization (SEM), ainsi qu\u2019\u00e9tudier la segmentation non supervis\u00e9e obtenue avec l\u2019estimateur du mode des marginales a posteriori (MPM). Les segmentations supervis\u00e9es et non supervis\u00e9es par MPM, bas\u00e9es sur la CMC avec CPS, sont compar\u00e9s aux HMC avec PS et aux HMF \u00e0 travers des exp\u00e9riences sur des images synth\u00e9tiques. Elles am\u00e9liorent de mani\u00e8re significative les premi\u00e8res, et peuvent m\u00eame \u00eatre comp\u00e9titives avec ces derniers. Finalement, nous \u00e9tendons les CMC-CPS aux cha\u00eenes de Markov couples conditionnelles (CPMC) et \u00e0 deux cha\u00eenes de Markov triplets particuli\u00e8res : les cha\u00eenes de Markov \u00e9videntielles conditionnelles (CEMC) et les cha\u00eenes de semi-Markov conditionnelles (CSMC). Pour chacune de ces extensions, nous montrons qu\u2019elles peuvent am\u00e9liorer de mani\u00e8re notable leur contrepartie non conditionnelle, ainsi que les CMC-CPS, et peuvent m\u00eame \u00eatre comp\u00e9titives avec les HMF. Par ailleurs, elles permettent de mieux utiliser la g\u00e9n\u00e9ralit\u00e9 du triplet markovien dans le cadre de la segmentation d\u2019image, en contournant les probl\u00e8mes de temps de calcul consid\u00e9rables qui apparaissent lorsque l\u2019on passe des champs de Markov cach\u00e9s aux triplets.<\/p>\n\n\n\n Hidden Markov chains (HMC) are widely used in unsupervised Bayesian hidden discrete data restoration. They are very robust and, in spite of their simplicity, they are sufficiently efficient in many situations. In particular for image segmentation, despite their mono-dimensional nature, they are able, through a transformation of the bi-dimensional images into mono-dimensional sequences with Peano scan (PS), to give satisfying results. However, sometimes, more complex models such as hidden Markov fields (HMF) may be preferred in spite of their increased time complexity, for their better results. Moreover, hidden Markov models (the chains as well as the fields) have been extended to pairwise and triplet Markov models, which can be of interest in more complex situations. For example, when sojourn time in hidden states is not geometrical, hidden semi-Markov (HSMC) chains tend to perform better than HMC, and such is also the case for hidden evidential Markov chains (HEMC) when data are non-stationary. In this thesis, we first propose a new triplet Markov chain (TMC), which simultaneously extends HSMC and HEMC. Based on hidden triplet Markov chains (HTMC), the new hidden evidential semi-Markov chain (HESMC) model can be used in unsupervised framework, parameters being estimated with Expectation-Maximization (EM) algorithm. We validate its interest through some experiments on synthetic data. Then we address the problem of mono-dimensionality of the HMC with PS model in image segmentation by introducing the \u201ccontextual\u201d Peano scan (CPS). It consists in associating to each index in the HMC obtained from PS, two observations on pixels which are neighbors of the pixel considered in the image, but are not its neighbors in the HMC. This gives three observations on each point of the Peano scan, which leads to a new conditional Markov chain (CMC) with a more complex structure, but whose posterior law is still Markovian. Therefore, we can apply the usual parameter estimation method: Stochastic Expectation-Maximization (SEM), as well as study unsupervised segmentation Marginal Posterior Mode (MPM) so obtained. The CMC with CPS based supervised and unsupervised MPM are compared to the classic scan based HMC-PS and the HMF through experiments on artificial images. They improve notably the former, and can even compete with the latter. Finally, we extend the CMC-CPS to Pairwise Conditional Markov (CPMC) chains and two particular triplet conditional Markov chain: evidential conditional Markov chains (CEMC) and conditional semi-Markov chains (CSMC). For each of these extensions, we show through experiments on artificial images that these models can improve notably their non conditional counterpart, as well as the CMC with CPS, and can even compete with the HMF. Beside they allow the generality of markovian triplets to better play its part in image segmentation, while avoiding the substantial time complexity of triplet Markov fields.<\/p>\n","protected":false},"excerpt":{"rendered":" L’Ecole doctorale : Math\u00e9matiques Hadamardet le Laboratoire de recherche SAMOVAR – Services r\u00e9partis, Architectures, MOd\u00e9lisation, Validation, Administration des R\u00e9seaux pr\u00e9sentent l\u2019AVIS DE SOUTENANCE de Monsieur Cl\u00e9ment FERNANDES Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Institut Polytechnique de Paris, pr\u00e9par\u00e9 \u00e0 T\u00e9l\u00e9com SudParis en : \u00ab Cha\u00eenes de Markov triplets et 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M. Nikolaos LIMNIOS<\/strong>, Professeur des universit\u00e9s, Universit\u00e9 de Technologie de Compi\u00e8gne, FRANCE – Examinateur
M. C\u00e9dric RICHARD<\/strong>, Professeur, Universit\u00e9 C\u00f4te d’Azur, FRANCE – Examinateur
M. Fran\u00e7ois SEPTIER<\/strong>, Professeur, Universit\u00e9 Bretagne Sud, FRANCE – Rapporteur
M. Jean-Yves TOURNERET<\/strong>, Professeur, ENSEEIHT, FRANCE – Rapporteur
Mme Florence TUPIN<\/strong>, Professeure, T\u00e9l\u00e9com Paris, FRANCE – Examinatrice
<\/p>\n\n\n\n
Abstract : \u00ab\u00a0Triplet Markov chains and unsupervised image segmentation\u00a0\u00bb<\/strong><\/p>\n\n\n\n